Optimizing the Jacobian in networks with more than one layer is cumbersome, thus very often the stochastic
approach is preferred over the analytic e.g. [1]}. Denoising autoencoders, [2]}
follow the stochastic paradigm and require that small random variations in the inputs have only a limited
effect on the model output. [3]}, [3]},
used Gaussian perturbations to stabilise the network's output with respect to variations in the input,
essentially augmenting the training data. Regularisers on higher order derivatives, Hessian,
are also used, [5]}, in such cases the stochastic approach is the only choice due to
the prohibitive cost of optimizing the Hessian term.
